TABLE OF OBJECTIVES AND OUTCOMES – CONTINUUM OF LEARNING IN MATHEMATICS K–10
Working Mathematically
Students:
•
develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communication and reasoning
Early Stage 1 outcomes
Stage 1 outcomes
Stage 2 outcomes
Stage 3 outcomes
Stage 4 outcomes
Stage 5.1 outcomes
Stage 5.2 outcomes
Stage 5.3 outcomes
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Communicating
MAe-1WM describes mathematical
situations using everyday language,
actions, materials and informal
recordings
Communicating
MA1-1WM describes mathematical
situations and methods using
everyday and some mathematical
language, actions, materials,
diagrams and symbols
Communicating
MA2-1WM uses appropriate
terminology to describe, and
symbols to represent, mathematical
ideas
Communicating
MA3-1WM describes and
represents mathematical situations
in a variety of ways using
mathematical terminology and
some conventions
Communicating
MA4-1WM communicates and
connects mathematical ideas using
appropriate terminology, diagrams
and symbols
Communicating
MA5.1-1WM uses appropriate
terminology, diagrams and symbols
in mathematical contexts
Communicating
MA5.2-1WM selects appropriate
notations and conventions to
communicate mathematical ideas
and solutions
Communicating
MA5.3-1WM uses and interprets
formal definitions and generalisations
when explaining solutions and/or
conjectures
Problem Solving
MAe-2WM uses objects, actions,
technology and/or trial and error to
explore mathematical problems
Problem Solving
MA1-2WM uses objects, diagrams
and technology to explore
mathematical problems
Problem Solving
MA2-2WM selects and uses
appropriate mental or written
strategies, or technology, to solve
problems
Problem Solving
MA3-2WM selects and applies
appropriate problem-solving
strategies, including the use of
digital technologies, in undertaking
investigations
Problem Solving
MA4-2WM applies appropriate
mathematical techniques to solve
problems
Problem Solving
MA5.1-2WM selects and uses
appropriate strategies to solve
problems
Problem Solving
MA5.2-2WM interprets mathematical
or real-life situations, systematically
applying appropriate strategies to
solve problems
Problem Solving
MA5.3-2WM generalises
mathematical ideas and techniques
to analyse and solve problems
efficiently
Reasoning
MAe-3WM uses concrete materials
and/or pictorial representations to
support conclusions
Reasoning
MA1-3WM supports conclusions by
explaining or demonstrating how
answers were obtained
Reasoning
MA2-3WM checks the accuracy of
a statement and explains the
reasoning used
Reasoning
MA3-3WM gives a valid reason for
supporting one possible solution
over another
Reasoning
MA4-3WM recognises and explains
mathematical relationships using
reasoning
Reasoning
MA5.1-3WM provides reasoning to
support conclusions that are
appropriate to the context
Reasoning
MA5.2-3WM constructs arguments
to prove and justify results
Reasoning
MA5.3-3WM uses deductive
reasoning in presenting arguments
and formal proofs
MATHEMATICS LEARNING IN STAGE 5
Intended Stage 6 Board Developed Course and recommended Stage 5 content (minimum)
Preliminary Mathematics General/
HSC Mathematics General 2
Mathematics ('2 Unit')
Mathematics Extension 1
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(substrands identified by ◊)
(substrands identified by §)
(optional substrands identified by #)
Number and Algebra
Students:
•
develop efficient strategies for numerical calculation, recognise patterns, describe relationships and apply algebraic techniques and generalisation
Early Stage 1 outcomes
Stage 1 outcomes
Stage 2 outcomes
Stage 3 outcomes
Stage 4 outcomes
Stage 5.1 outcomes
Stage 5.2 outcomes
Stage 5.3 outcomes
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Whole Numbers
MAe-4NA counts to 30, and orders,
reads and represents numbers in
the range 0 to 20
Whole Numbers
MA1-4NA applies place value,
informally, to count, order, read and
represent two- and three-digit
numbers
Whole Numbers
MA2-4NA applies place value to
order, read and represent numbers
of up to five digits
Whole Numbers
MA3-4NA orders, reads and
represents integers of any size and
describes properties of whole
numbers
Addition and Subtraction
MAe-5NA combines, separates and
compares collections of objects,
describes using everyday language,
and records using informal methods
Addition and Subtraction
MA1-5NA uses a range of
strategies and informal recording
methods for addition and
subtraction involving one- and twodigit numbers
Addition and Subtraction
MA2-5NA uses mental and written
strategies for addition and
subtraction involving two-, three-,
four- and five-digit numbers
Addition and Subtraction
MA3-5NA selects and applies
appropriate strategies for addition
and subtraction with counting
numbers of any size
Multiplication and Division
MAe-6NA groups, shares and
counts collections of objects,
describes using everyday language,
and records using informal methods
Multiplication and Division
MA1-6NA uses a range of mental
strategies and concrete materials
for multiplication and division
Multiplication and Division
MA2-6NA uses mental and informal
written strategies for multiplication
and division
Multiplication and Division
MA3-6NA selects and applies
appropriate strategies for
multiplication and division, and
applies the order of operations to
calculations involving more than
one operation
Fractions and Decimals
MAe-7NA describes two equal
parts as halves
Fractions and Decimals
MA1-7NA represents and models
halves, quarters and eighths
Fractions and Decimals
MA2-7NA represents, models and
compares commonly used fractions
and decimals
Fractions, Decimals and
Percentages
MA3-7NA compares, orders and
calculates with fractions, decimals
and percentages
Computation with Integers
MA4-4NA compares, orders and
calculates with integers, applying a
range of strategies to aid
computation
Fractions, Decimals and
Percentages
MA4-5NA operates with fractions,
decimals and percentages
Financial Mathematics
Financial Mathematics
Financial Mathematics ◊
MA4-6NA solves financial problems MA5.1-4NA solves financial
MA5.2-4NA solves financial
involving purchasing goods
problems involving earning, spending problems involving compound
and investing money
interest
Patterns and Algebra
MAe-8NA recognises, describes
and continues repeating patterns
Patterns and Algebra
MA1-8NA creates, represents and
continues a variety of patterns with
numbers and objects
Patterns and Algebra
MA2-8NA generalises properties of
odd and even numbers, generates
number patterns, and completes
simple number sentences by
calculating missing values
Patterns and Algebra
MA3-8NA analyses and creates
geometric and number patterns,
constructs and completes number
sentences, and locates points on
the Cartesian plane
Ratios and Rates
MA4-7NA operates with ratios and
rates, and explores their graphical
representation
Ratios and Rates
MA5.2-5NA recognises direct and
indirect proportion, and solves
problems involving direct proportion
Ratios and Rates
MA5.3-4NA draws, interprets and
analyses graphs of physical
phenomena
Algebraic Techniques
MA4-8NA generalises number
properties to operate with algebraic
expressions
Algebraic Techniques
MA5.2-6NA simplifies algebraic
fractions, and expands and
factorises quadratic expressions
Algebraic Techniques §
MA5.3-5NA selects and applies
appropriate algebraic techniques to
operate with algebraic expressions
Indices
MA5.2-7NA applies index laws to
operate with algebraic expressions
involving integer indices
Surds and Indices §
MA5.3-6NA performs operations with
surds and indices
Equations
MA5.2-8NA solves linear and simple
quadratic equations, linear
inequalities and linear simultaneous
equations, using analytical and
graphical techniques
Equations §
MA5.3-7NA solves complex linear,
quadratic, simple cubic and
simultaneous equations, and
rearranges literal equations
Indices
MA4-9NA operates with positiveinteger and zero indices of numerical
bases
Equations
MA4-10NA uses algebraic
techniques to solve simple linear and
quadratic equations
Indices
MA5.1-5NA operates with algebraic
expressions involving positiveinteger and zero indices, and
establishes the meaning of negative
indices for numerical bases
Early Stage 1 outcomes
Stage 1 outcomes
Stage 2 outcomes
Stage 3 outcomes
Stage 4 outcomes
Stage 5.1 outcomes
Stage 5.2 outcomes
Stage 5.3 outcomes
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Linear Relationships
MA4-11NA creates and displays
number patterns; graphs and
analyses linear relationships; and
performs transformations on the
Cartesian plane
Linear Relationships
Linear Relationships
MA5.1-6NA determines the midpoint, MA5.2-9NA uses the gradientgradient and length of an interval,
intercept form to interpret and graph
and graphs linear relationships
linear relationships
Linear Relationships §
MA5.3-8NA uses formulas to find
midpoint, gradient and distance on
the Cartesian plane, and applies
standard forms of the equation of a
straight line
Non-Linear Relationships
Non-Linear Relationships ◊
Non-Linear Relationships §
MA5.1-7NA graphs simple non-linear MA5.2-10NA connects algebraic and MA5.3-9NA sketches and interprets
relationships
graphical representations of simple a variety of non-linear relationships
non-linear relationships
Polynomials #
MA5.3-10NA recognises, describes
and sketches polynomials, and
applies the factor and remainder
theorems to solve problems
Logarithms #
MA5.3-11NA uses the definition of a
logarithm to establish and apply the
laws of logarithms
Functions and Other Graphs #
MA5.3-12NA uses function notation
to describe and sketch functions
Measurement and Geometry
Students:
•
identify, visualise and quantify measures and the attributes of shapes and objects, and explore measurement concepts and geometric relationships, applying formulas, strategies and geometric reasoning in the solution of problems
Early Stage 1 outcomes
Stage 1 outcomes
Stage 2 outcomes
Stage 3 outcomes
Stage 4 outcomes
Stage 5.1 outcomes
Stage 5.2 outcomes
Stage 5.3 outcomes
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Length
MAe-9MG describes and compares
lengths and distances using
everyday language
Length
MA1-9MG measures, records,
compares and estimates lengths
and distances using uniform
informal units, metres and
centimetres
Length
MA2-9MG measures, records,
compares and estimates lengths,
distances and perimeters in metres,
centimetres and millimetres, and
measures, compares and records
temperatures
Length
MA3-9MG selects and uses the
appropriate unit and device to
measure lengths and distances,
calculates perimeters, and converts
between units of length
Length
MA4-12MG calculates the
perimeters of plane shapes and the
circumferences of circles
Area
MAe-10MG describes and
compares areas using everyday
language
Area
MA1-10MG measures, records,
compares and estimates areas
using uniform informal units
Area
MA2-10MG measures, records,
compares and estimates areas
using square centimetres and
square metres
Area
MA3-10MG selects and uses the
appropriate unit to calculate areas,
including areas of squares,
rectangles and triangles
Area
MA4-13MG uses formulas to
calculate the areas of quadrilaterals
and circles, and converts between
units of area
Area and Surface Area
MA5.1-8MG calculates the areas of
composite shapes, and the surface
areas of rectangular and triangular
prisms
Area and Surface Area
MA5.2-11MG calculates the surface
areas of right prisms, cylinders and
related composite solids
Area and Surface Area
MA5.3-13MG applies formulas to
find the surface areas of right
pyramids, right cones, spheres and
related composite solids
Volume and Capacity
MAe-11MG describes and
compares the capacities of
containers and the volumes of
objects or substances using
everyday language
Volume and Capacity
MA1-11MG measures, records,
compares and estimates volumes
and capacities using uniform
informal units
Volume and Capacity
MA2-11MG measures, records,
compares and estimates volumes
and capacities using litres, millilitres
and cubic centimetres
Volume and Capacity
MA3-11MG selects and uses the
appropriate unit to estimate,
measure and calculate volumes and
capacities, and converts between
units of capacity
Volume
MA4-14MG uses formulas to
calculate the volumes of prisms and
cylinders, and converts between
units of volume
Volume
MA5.2-12MG applies formulas to
calculate the volumes of composite
solids composed of right prisms and
cylinders
Volume
MA5.3-14MG applies formulas to
find the volumes of right pyramids,
right cones, spheres and related
composite solids
Mass
MAe-12MG describes and
compares the masses of objects
using everyday language
Mass
MA1-12MG measures, records,
compares and estimates the
masses of objects using uniform
informal units
Mass
MA2-12MG measures, records,
compares and estimates the
masses of objects using kilograms
and grams
Mass
MA3-12MG selects and uses the
appropriate unit and device to
measure the masses of objects,
and converts between units of
mass
Time
MAe-13MG sequences events,
uses everyday language to describe
the durations of events, and reads
hour time on clocks
Time
MA1-13MG describes, compares
and orders durations of events, and
reads half- and quarter-hour time
Time
MA2-13MG reads and records time
in one-minute intervals and
converts between hours, minutes
and seconds
Time
MA3-13MG uses 24-hour time and
am and pm notation in real-life
situations, and constructs timelines
Three-Dimensional
Space
MAe-14MG manipulates, sorts and
represents three-dimensional
objects and describes them using
everyday language
Three-Dimensional
Space
MA1-14MG sorts, describes,
represents and recognises familiar
three-dimensional objects,
including cones, cubes, cylinders,
spheres and prisms
Three-Dimensional
Space
MA2-14MG makes, compares,
sketches and names threedimensional objects, including
prisms, pyramids, cylinders, cones
and spheres, and describes their
features
Three-Dimensional
Space
MA3-14MG identifies threedimensional objects, including
prisms and pyramids, on the basis
of their properties, and visualises,
sketches and constructs them
given drawings of different views
Two-Dimensional Space
MAe-15MG manipulates, sorts and
describes representations of twodimensional shapes, including
circles, triangles, squares and
rectangles, using everyday
language
Two-Dimensional
Space
MA1-15MG manipulates, sorts,
represents, describes and explores
two-dimensional shapes, including
quadrilaterals, pentagons,
hexagons and octagons
Two-Dimensional
Space
MA2-15MG manipulates, identifies
and sketches two-dimensional
shapes, including special
quadrilaterals, and describes their
features
Two-Dimensional
Space
MA3-15MG manipulates, classifies
and draws two-dimensional
shapes, including equilateral,
isosceles and scalene triangles, and
describes their properties
Time
MA4-15MG performs calculations of
time that involve mixed units, and
interprets time zones
Numbers of Any Magnitude
MA5.1-9MG interprets very small
and very large units of measurement,
uses scientific notation, and rounds
to significant figures
Right-Angled Triangles
(Pythagoras)
MA4-16MG applies Pythagoras’
theorem to calculate side lengths in
right-angled triangles, and solves
related problems
Right-Angled Triangles
(Trigonometry)
MA5.1-10MG applies trigonometry,
given diagrams, to solve problems,
including problems involving angles
of elevation and depression
Right-Angled Triangles
Trigonometry and Pythagoras'
(Trigonometry) ◊
Theorem §
MA5.2-13MG applies trigonometry to MA5.3-15MG applies Pythagoras’
solve problems, including problems theorem, trigonometric relationships,
involving bearings
the sine rule, the cosine rule and the
area rule to solve problems,
including problems involving three
dimensions
Properties of Geometrical Figures
MA4-17MG classifies, describes and
uses the properties of triangles and
quadrilaterals, and determines
congruent triangles to find unknown
side lengths and angles
Properties of Geometrical Figures
MA5.1-11MG describes and applies
the properties of similar figures and
scale drawings
Properties of Geometrical Figures
MA5.2-14MG calculates the angle
sum of any polygon and uses
minimum conditions to prove
triangles are congruent or similar
Properties of Geometrical
Figures §
MA5.3-16MG proves triangles are
similar, and uses formal geometric
reasoning to establish properties of
triangles and quadrilaterals
Early Stage 1 outcomes
Stage 1 outcomes
Stage 2 outcomes
Stage 3 outcomes
Stage 4 outcomes
Stage 5.1 outcomes
Stage 5.2 outcomes
Stage 5.3 outcomes
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Angles
MA2-16MG identifies, describes,
compares and classifies angles
Angles
MA3-16MG measures and
constructs angles, and applies
angle relationships to find unknown
angles
Angle Relationships
MA4-18MG identifies and uses angle
relationships, including those related
to transversals on sets of parallel
lines
Position
MA2-17MG uses simple maps and
grids to represent position and
follow routes, including using
compass directions
Position
MA3-17MG locates and describes
position on maps using a gridreference system
Position
MAe-16MG describes position and
gives and follows simple directions
using everyday language
Position
MA1-16MG represents and
describes the positions of objects in
everyday situations and on maps
Circle Geometry #
MA5.3-17MG applies deductive
reasoning to prove circle theorems
and to solve related problems
Statistics and Probability
Students:
•
collect, represent, analyse, interpret and evaluate data, assign and use probabilities, and make sound judgements
Early Stage 1 outcomes
Stage 1 outcomes
Stage 2 outcomes
Stage 3 outcomes
Stage 4 outcomes
Stage 5.1 outcomes
Stage 5.2 outcomes
Stage 5.3 outcomes
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Data
MAe-17SP represents data and
interprets data displays made from
objects
Data
MA1-17SP gathers and organises
data, displays data in lists, tables
and picture graphs, and interprets
the results
Data
MA2-18SP selects appropriate
methods to collect data, and
constructs, compares, interprets
and evaluates data displays,
including tables, picture graphs and
column graphs
Data
MA3-18SP uses appropriate
methods to collect data and
constructs, interprets and evaluates
data displays, including dot plots,
line graphs and two-way tables
Data Collection and
Representation
MA4-19SP collects, represents and
interprets single sets of data, using
appropriate statistical displays
Single Variable Data Analysis
MA5.1-12SP uses statistical displays
to compare sets of data, and
evaluates statistical claims made in
the media
Single Variable Data Analysis ◊
Single Variable Data Analysis
MA5.2-15SP uses quartiles and box MA5.3-18SP uses standard deviation
plots to compare sets of data, and
to analyse data
evaluates sources of data
Single Variable Data Analysis
MA4-20SP analyses single sets of
data using measures of location, and
range
Bivariate Data Analysis
MA5.2-16SP investigates
relationships between two statistical
variables, including their relationship
over time
Chance
MA1-18SP recognises and
describes the element of chance in
everyday events
Chance
MA2-19SP describes and
compares chance events in social
and experimental contexts
Chance
MA3-19SP conducts chance
experiments and assigns
probabilities as values between
0 and 1 to describe their outcomes
Probability
MA4-21SP represents probabilities
of simple and compound events
Probability
MA5.1-13SP calculates relative
frequencies to estimate probabilities
of simple and compound events
Probability
MA5.2-17SP describes and
calculates probabilities in multi-step
chance experiments
Bivariate Data Analysis
MA5.3-19SP investigates the
relationship between numerical
variables using lines of best fit, and
explores how data is used to inform
decision-making processes